Section: Overall Objectives

Build, simulate and analyze models of microbial ecosystems

We investigate different models of microbial ecosystems at various scales, depending on the observations reported by biologists and questions of interest. The models we intend to develop and study cover the usual three scales of ecology: the individual in its community, the community in interaction with its environment and the overall ecosystem.

The main questions we address concern the roles of biotic and abiotic interactions on the coexistence or exclusion of species, the behavior of transient dynamics and the performances of bio-processes.

For this purpose, we build population models both deterministic (differential equations) and stochastic (stochastic differential equations, birth and death processes), as well as individual-based models (usually stochastic). We study their dynamical properties combining mathematical analysis (determination of equilibria and their stability, construction of Lyapunov functions, analysis of limit cycles, weak convergence between models...) and numerical simulations (Monte-Carlo techniques, Gillespie-like algorithms...). Some of our models include spatial considerations, with explicit (transport and/or diffusion terms) or implicit (compartments or “gradostat”-like equations) representations.

We aim at determining the validity and the effective limits of these models, and at developing tools for change of scales (e.g. from an individual-based model to a deterministic macroscopic model and vice-versa). We consider also multi-scale modeling, for instance in biofilm simulations for which the scale of micro-organisms and the scale of the exo-polymer matrix impact each other. The scope of our research program stops at the individual level as its smallest level. We do not intend to model the mechanisms inside micro-organisms but rather to focus on populations, and especially on the effects of large numbers of individuals sharing the same environment.